How many positive factors does the positive integer x have?

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution

How many positive factors does the positive integer x have?

(1) x is the product of 3 distinct prime numbers.

(2) x and 3^7 have the same number of positive factors.

There is 1 variable (x) in the original condition. In order to match the number of variables and the number of equations, we need 1 equation. Since the condition 1) and 2) each has 1 equation, there is high chance that D is the answer.

In case of the condition 1), we can get x=2*3*5. The number of distinct factors is (1+1)(1+1)(1+1)=8. The answer is unique and the condition is sufficient.
In case of the condition 2), if x and 3^7 have the same number of positive factors, then the number of distinct factors is (7+1)=8. The answer is unique and the condition is sufficient. Therefore, the answer is D.


For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

Hi Bunuel ,

I have doubt in Statement .. How can statement 1 be sufficient .

As per my understanding ...

(1) x is the product of 3 distinct prime numbers.

x is product of 3 distinct prime ...but the power of prime is not known .

Please advise .

Regards

We cannot say that 2*3^2*5 is a product of 3 distinct primes. The first statement implies that x = prime*prime*prime.

HI brunel,

I am still having some trouble understanding statement 1:

1) x is the product of 3 distinct prime numbers.

in the example above we used 2x3x5 = 30 (this has 8 positive factors)

what is we use 1x2x3 = 6 ( This has 4 different factors)

wouldn't this make statement 1 insufficient?

1 is not a prime number.

Nice One
Here statement 1 is sufficient as the number of prime factors = product of powers of primes after raising them by 1
hence sufficient
statement 2 is sufficient as Number of factors =8
hence D

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